This book is mainly devoted to the combinatorics of quadratic holomorphic dynamics. The conceptual kernel is a self-contained abstract counterpart of connected quadratic Julia sets which is built on Thurston's concept of a quadratic invariant lamination and on symbolic descriptions of the angle-doubling map. The theory obtained is illustrated in the complex plane. It is used to give rigorous proofs of some well-known and some partially new statements on the structure of the Mandelbrot set. The text is intended for graduate students and researchers. Some elementary knowledge in topology and in functions of one complex variable is assumed.

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Bibliographic Information

Book Title: Invariant Factors, Julia Equivalences and the (Abstract) Mandelbrot Set
Authors: Karsten Keller
Series Title: Lecture Notes in Mathematics
DOI: https://doi.org/10.1007/BFb0103999
Publisher: Springer Berlin, Heidelberg
eBook Packages: Springer Book Archive
Copyright Information: Springer-Verlag Berlin Heidelberg 2000
Softcover ISBN: 978-3-540-67434-4Published: 06 May 2000
eBook ISBN: 978-3-540-45589-9Published: 06 May 2007
Series ISSN: 0075-8434
Series E-ISSN: 1617-9692
Edition Number: 1
Number of Pages: XII, 208
Topics: Partial Differential Equations, Topology

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Table of contents (4 chapters)

Front Matter

Introduction

Abstract Julia sets

The Abstract Mandelbrot set

Abstract and concrete theory

Back Matter

About this book